Combine the red rice, 3 cups water and 1/2 teaspoon salt in a medium saucepan. Cover and bring to a simmer over medium heat. Reduce the heat to medium low and cook until the rice is tender, about 45 minutes. (Drain any excess water.)
Meanwhile, heat the olive oil in a large deep skillet over medium-high heat. Add the onion; sprinkle with the sugar and season with salt and pepper. Cook, stirring, until the onion is soft, about 5 minutes. Add the ginger and dried cherries; cook, stirring, until the onion is golden brown, about 7 more minutes.
Stir the prepared rice into the onion mixture. Add the baby spinach and orange juice and stir until the spinach is just wilted, about 1 minute. Season with salt and pepper.